Method and apparatus for encoding 3d mesh models, and method and apparatus for decoding encoded 3d mesh models

ABSTRACT

3D mesh models are widely used in various applications for representing 3D objects. These models are made of vertices and corresponding triangles, which can be compressed based on prediction and residuals. The present invention improves the accuracy of parallelogram prediction, particularly near sharp features. The proposed 3D mesh model encoding comprises analyzing the spatial or dihedral angles between triangles, clustering triangles with similar or equal dihedral angles, and defining a representative dihedral angle for each cluster. Triangles of each cluster are then encoded relative to individual prediction triangles having the representative dihedral angle according to the cluster. Additionally, the prediction triangle may be mirrored. An indication of the encoding mode is inserted into each vertex of the encoded bitstream. A decoder extracts the encoding mode indication, reconstructs the individual prediction triangles based on the respective representative dihedral angles and performs triangle prediction and reconstruction.

FIELD OF THE INVENTION

This invention relates to a method and an apparatus for encoding 3D meshmodels, and a method and an apparatus for decoding encoded 3D meshmodels.

BACKGROUND OF THE INVENTION

Three-dimensional (3D) meshes are widely used in various applicationsfor representing 3D objects, such as video games, engineering design,e-commerce, virtual reality, and architectural and scientificvisualization. Usually their raw representation requires a huge amountof data. However, most applications prefer compact 3D meshrepresentation for storage or transmission. Various algorithms have beenproposed since the early 1990s for efficiently compressing 3D meshes,e.g. “Technologies for 3D mesh compression: A survey”, by JingliangPeng, Chang-Su Kim, C.-C. Jay Kuo, ELSEVIER Journal of VisualCommunication and Image Representation, 2005, pp. 688-733. Moreover, arapidly growing demand for 3D mesh models can be expected due tointernet based 3D applications, e.g. games.

Typically, 3D meshes are represented by three types of data:connectivity data, geometry data and property data. Connectivity datadescribe the adjacency relationship between vertices, geometry dataspecify vertex locations, and property data specify attributes such asthe normal vector, material reflectance and texture coordinates. Most 3Dcompression algorithms compress connectivity data and geometry dataseparately. The coding order of geometry data is determined by theunderlying connectivity coding. Geometry data is usually compressed bythree main steps: quantization, prediction and statistical encoding. 3Dmesh property data are usually compressed in a similar manner.

The prediction step exploits the correlation between adjacent vertexpositions, which is most crucial in improving geometry compressionefficiency. The most widely used prediction strategy is parallelogramprediction, as proposed by literature [TG98] (C. Touma, C. Gotsman:“Triangle mesh compression”, Proceedings of Graphics Interface, 1998,pp. 26-34). This approach is shown in FIG. 1. The shaded area hasalready been encoded/decoded. The position of a new vertex r ispredicted by the reference triangle Δuvw using the equation

r ^(p) =u+v−w  (Eq.1)

Parallelogram prediction is based on the assumption that the fourvertices u,v,w,r, are co-planar and construct a flat parallelogram.However, this basic assumption is not always true. In FIG. 1, there is aspatial angle θ between the reference triangle Δuvw and the new,so-called spanning triangle Δurv. This spatial angle, referred to asdihedral angle, is encoded. It defines the rotation of the spanningtriangle Δurv around the common side uv that the reference triangleΔuvw, the co-planar prediction triangle Δur^(p)v and the spanningtriangle Δurv have. The prediction error or residual between thepredicted vertex r^(p) and the actual vertex r can be expressed as avector res_(p).

Even for a simple model, such as a box shown in FIG. 2, the residualafter parallelogram prediction may be quite big: the difference vectorres_(p) between the predicted vertex r^(p) and the actual vertex r iseven longer than a box side.

Typical failure cases are shown in FIG. 3 a). Triangles of theencoded/decoded area A_(ed) are usually not co-planar. In one failurecase, the new vertex c is not in the same plane with the referencetriangle Δabd. Thus, the residual C1 is significant. Also in anotherfailure case there is a significant difference C2 between a predictedposition h^(p) and an actual vertex h, although the new vertex h is inthe same plane as the reference triangle Δfeg. To improve the predictionaccuracy, [TG98] uses the dihedral angle θ shown in FIG. 3 b) betweenΔebg and Δbdg to predict the neighboring dihedral angle between Δadb andΔabc. Another approach¹ uses a multi-way parallelogram prediction schemeshown in FIG. 4. The multi-way prediction exploits all possiblereference triangles and uses the average of all single-way predictedpositions as the multi-way prediction result. [GA03]² and [LAM02]³divide vertex positions into tangential coordinates and dihedral angles,as shown in FIG. 5. The dihedral angle between the reference triangleand spanning triangle is predicted and encoded using this kind of localcoordinate system. [GA03] fits a higher order surface to the encodedvertices and uses the high order surface to predict the dihedral angleα. ¹ D. Cohen-Or, R. Cohen, and R. Irony: “Multiway geometry encoding”,Technical report, School of Computer Science, Tel Aviv University, 2002²S. Gumhold, R. Amjoun: “Higher order prediction of geometrycompression”, Proceedings of the Shape Modeling International, Seoul,2003, 59˜66³ H. Lee, O. Allidz, M. Desbrun: “Angle-analyzer: Atriangle-quad mesh codec”, Eurographics Conference Proceedings, 2002,383˜392

Although many algorithms have been proposed to improve the accuracy ofparallelogram prediction, vertices near sharp features, i.e. the areawith highly varying curvature, still have relatively large residuals.The corresponding dihedral angles can not be deduced well from thereference triangles which are usually on the opposite side of the sharpfeature. Most prediction schemes constrain the reference triangles to beon the same smooth surface as the spanning triangle, ie. the one thatincludes the actual new vertex. Although [GA03] works on making accurateprediction of the dihedral angle α, the vertices for fitting the highorder surface are restricted in the already encoded and nearly flatregion around the reference triangle, and the extra high order surfacefitting step also significantly decreases the speed of both geometryencoder and decoder.

To improve geometry compression efficiency particularly of 3D mesheswith lots of sharp features, such as typical 3D engineering models, anefficient prediction strategy specially designed for vertices on sharpfeatures is needed.

SUMMARY OF THE INVENTION

The present invention is based on the recognition of the fact that inmany 3D mesh models certain ranges of dihedral angles are used much morefrequently than others. Thus, it is possible during encoding to reduceredundancy.

In principle, the invention comprises in one aspect steps of analyzingthe dihedral angles between adjacent triangles of a 3D mesh, wherein itis determined that many of the dihedral angles are equal orsubstantially equal, defining at least one range of dihedral anglesaround said equal or substantially equal dihedral angles and defining acorresponding representative dihedral angle, and encoding dihedralangles that are equal or substantially equal to the representativedihedral angle relative to the representative dihedral angle. Otherdihedral angles may be encoded conventionally, or clustered into anotherrange with another representative. An indication of the encoding mode isinserted into the triangles of the encoded 3D mesh. Only those dihedralangles between spanning triangles and their respective referencetriangles need to be considered.

In another aspect, the invention comprises in principle steps ofdetermining a representative dihedral angle, extracting from an encoded3D mesh an indication of the encoding mode of a spanning triangle, anddepending on the indication reconstructing the spanning triangle basedon either only the reference triangle, or based on the referencetriangle and a prediction triangle, wherein the dihedral angle betweenthe reference triangle and the prediction triangle is saidrepresentative dihedral angle.

The present invention is suitable for increasing coding efficiency andimproving prediction accuracy, especially on 3D meshes with many sharpfeatures, such as 3D engineering models. This makes a geometry codermuch more efficient. The invention can be used for encoding trianglesthat are in different spatial planes, and in particular encoding theirdihedral angles, based on prediction.

According to one aspect of the invention, a method for encoding a 3Dmesh model composed of triangles represented by connectivity data,geometry data and property data comprises steps of determining pairs oftriangles, each pair having a reference triangle and a triangle to bepredicted, wherein both triangles have a common side along a first axis,for each of said pairs of triangles, determining a dihedral anglebetween the reference triangle and the triangle to be predicted,analyzing for the 3D mesh model the dihedral angles of the pairs oftriangles and, based on said analyzing, defining at least a first rangeof dihedral angles, wherein a plurality of said dihedral angles arewithin the first range of dihedral angles, defining for said first rangeof dihedral angles a first representative dihedral angle, encoding thetriangles of the 3D mesh model, wherein residuals between referencetriangles and corresponding predicted triangles are determined andencoded, and wherein if the dihedral angle between a reference triangleand a corresponding predicted triangle is within the first range ofdihedral angles, said encoding uses prediction based on an enhancedprediction triangle, wherein the dihedral angle between the referencetriangle and the enhanced prediction triangle is said representativedihedral angle, calculating and encoding a residual between saidtriangle to be predicted and said enhanced prediction triangle, andassociating with the encoded residual an indication indicating that itrefers to said representative dihedral angle.

One aspect of the invention concerns a corresponding apparatus forencoding 3D mesh models.

In one embodiment of the encoding method, a first enhanced predictiontriangle of a first mode and a second enhanced prediction triangle of asecond mode are mirrored along a co-planar second axis that isorthogonal to said first axis, and a second indication is associatedwith the encoded residual. The second indication indicates whether theresidual refers to the prediction triangle of the first or the secondmode.

In one embodiment of the encoding method, in the first mode the enhancedprediction triangle corresponds to a co-planar parallelogram extensionof the reference triangle that is rotated by said representativedihedral angle on the first axis, and wherein the enhanced predictiontriangles of the first and second mode are co-planar and both have saidside along the first axis common with the reference triangle.

According to another aspect of the invention, a signal comprises anencoded 3D mesh model composed of triangles, the encoded 3D mesh modelcomprising residual data for a plurality of triangles, wherein theresidual data are suitable for reconstructing a next triangle based on areference triangle, wherein the reference triangle and the next trianglehave a common side, and wherein the residual data comprise an indicationindicating that the encoding of the next triangle is relative to aprediction triangle also having said common side, wherein the dihedralangle between the prediction triangle and the reference triangle is apredefined dihedral angle.

In one embodiment of the signal aspect of the invention, the residualdata further comprise an indication indicating whether said encodingrefers to a first or a second prediction triangle, wherein the secondprediction triangle (T_(adv) _(—) _(pred2)) can be obtained from thefirst prediction triangle (T_(adv) _(—) _(pred1)) by mirroring orrotating along a co-planar axis (Y) that is orthogonal on said commonside. In one embodiment of the signal aspect, the signal furthercomprises the value of said predefined dihedral angle.

According to yet another aspect of the invention, a method for decodingan encoded 3D mesh model being composed of triangles comprises steps ofdetermining a first representative dihedral angle, extracting from theencoded 3D mesh model residual data relating to a reference triangle andto a next triangle to be reconstructed, wherein the data have associatedan indication indicating a coding mode, decoding from the residual dataa residual comprising a residual triangle or residual vector,reconstructing the triangle to be reconstructed based on a predictionfrom said reference triangle, wherein the reference triangle and thereconstructed triangle have a common side along a first axis, andwherein in response to said indication a prediction mode is used thatcomprises combining the residual with a predefined prediction triangle,wherein the dihedral angle between the reference triangle and thepredefined prediction triangle is said first representative dihedralangle.

One aspect of the invention concerns a corresponding apparatus fordecoding 3D mesh models.

In one embodiment of the decoding method, in a first prediction mode theresidual is added to a first prediction triangle and in a secondprediction mode the residual is added to a second prediction triangle,the first and second prediction triangles having a common side with thereference triangle along said first axis and being mirrored on a secondaxis that is orthogonal to said first axis.

Preferably, the prediction triangle can be generated by constructing anauxiliary triangle as a parallelogram extension of the referencetriangle. The reference triangle and the corresponding auxiliarytriangle are co-planar, so that the dihedral angle between each of themand the spanning triangle to be encoded is the same. In the next step,the auxiliary triangle is rotated around the axis of the common sidethat the reference triangle and the auxiliary triangle have. However,although this method is optimized for many existing 3D mesh models,there are generally also other methods usable for constructingprediction triangles, depending on the mesh elements of the 3D meshmodel.

Advantageous embodiments of the invention are disclosed in the dependentclaims, the following description and the figures.

BRIEF DESCRIPTION OF THE DRAWINGS

Exemplary embodiments of the invention are described with reference tothe accompanying drawings, which show in

FIG. 1 conventional parallelogram prediction;

FIG. 2 a 3D mesh model of a box that uses conventional parallelogramprediction;

FIG. 3 typical failure cases of parallelogram prediction;

FIG. 4 multi-way parallelogram prediction;

FIG. 5 a conventional local coordinate system;

FIG. 6 a geometry encoder with parallelogram predictor;

FIG. 7 a geometry decoder with parallelogram predictor;

FIG. 8 improved parallelogram prediction using a representative dihedralangle;

FIG. 9 a 3D mesh model of a box that uses improved parallelogramprediction;

FIG. 10 the principle of improved triangle prediction using mirroredprediction triangles;

FIG. 11 improved triangle prediction using multiple differentrepresentative dihedral angles and mirrored prediction triangles;

FIG. 12 an example of a 3D mesh model; and

FIG. 13 a prediction mode histogram of the exemplary 3D mesh model.

DETAILED DESCRIPTION OF THE INVENTION

The invention relates to an advanced prediction scheme for furtherimproving the prediction accuracy during geometry compression of 3Dmeshes. The dihedral angles between each pair of reference and spanningtriangles are analyzed, and frequently used dihedral angles are detectedand clustered. That is, one or more clusters are created depending onthe dihedral angles used in the current 3D mesh model, such that many ofthe dihedral angles fall into a cluster. For each cluster, arepresentative angle is defined. If many of the dihedral angles fallinto a cluster, the representative angle of such cluster is used todefine the prediction mode. An encoder will choose the proper predictionmode for each vertex. The predicted position is generated by a rotationoperation and, in one embodiment, by an additional mirror mappingoperation after traditional parallelogram prediction. The rotation angleand whether to do the mirror mapping are decided according to theprediction mode.

In the following, various embodiments of the invention are described.FIG. 8 shows an example of the prediction scheme that is based on anadvanced prediction triangle instead of a conventional flat predictiontriangle.

The advanced prediction triangle, as defined by one side uv of thereference triangle T_(ref) (or Δuvw) and an advanced predicted vertexr^(AdvPred), is used to predict the spanning triangle T_(span) (orΔurv), which is defined by said side uv of the reference triangle andthe actual vertex r. As can be seen, the residual (i.e. the predictionerror) between r and r^(AdvPred) is much smaller than that between r andthe conventionally predicted vertex r^(Pred). The additional cost forencoding the dihedral angle α is minimized by using the below-describedangle clustering. Therefore the actual vertex is cheaper to encode usingthe advanced predicted vertex, since it uses less data. Still the shapeof the advanced prediction triangle T_(AdvPred) is the same as that ofthe auxiliary triangle (Δur^(Pred)v), i.e. they have the same angles andside lengths (in below-described embodiments with two advancedprediction triangles, this is still true, since both are mirrored, i.e.two angles and two sides are just exchanged). The shape of the spanningtriangle T_(Span) however may be different. It is to be noted here thatthe reference triangle T_(ref) and the auxiliary triangle Δur^(Pred)vare co-planar, whereas the advanced prediction triangle _(AdvPred)(Δur^(AdvPred)v) has a dihedral angle α against them. In one embodiment,the advanced prediction triangle T_(Advpred) and the spanning triangleT_(span) have substantially the same dihedral angle α against thereference plane of T_(ref). In another embodiment, as described below,the dihedral angle of the spanning triangle may differ from the dihedralangle of the advanced prediction triangle within a defined, small range.

Along the vertex ordering dictated by connectivity coding, a geometryencoder according to one aspect of the invention first calculates thedihedral angles between pairs of a reference and a spanning triangleeach. The possible gain is calculated for a prediction residual thatremains after rotating the predicted position to (substantially) thesame plane as the spanning triangle, and optionally additional mirrormapping along the local Y axis. The local Y axis corresponds with theside common to the reference triangle and the spanning triangle. Thenall the dihedral angles are analyzed using angle clustering: clustersare adaptively defined according to the actual distribution of angles,similar or equal angles are assigned to a cluster, and the number ofangles in each cluster is determined.

In one exemplary embodiment, clusters are sorted by the number ofvertices falling into them, in decreasing order. If the first severalclusters are dominant, i.e. including most of the vertices, and the gainof advanced prediction residual is relative large compared to theconventional prediction residual, the advanced parallelogram predictionscheme according to the invention is used for geometry encoding. Therepresentative dihedral angles of the first several clusters define theprediction modes. In principle, one cluster is enough, but depending onthe 3D mesh model, the efficiency may be higher with more clusters.Otherwise, if the dihedral angles of the 3D mesh model are evenly spreadover a wide range, the traditional parallelogram prediction may bebetter.

Then the geometry data are compressed. If the advanced parallelogramprediction scheme is adopted, the advanced parallelogram predictor willfirst choose a prediction mode. Advantageously, it will choose for eachvertex to be encoded the prediction mode that generates the smallestresidual. The new vertex is predictively encoded with a rotation by therepresentative dihedral angle of the cluster, and optionally a mirrormapping step.

FIG. 9 shows an example where it is advantageous to use mirror mapping.The 3D mesh model is a (substantially) rectangular box. An analysis ofthe dihedral angles results in the definition of a cluster around arepresentative angle of 270 degrees. A reference triangle T_(ref) ismapped to a co-planar auxiliary triangle Δur^(Pred)v, which is thenrotated by the representative dihedral angle around the common side ofboth triangles, i.e. the local X axis. The first predicted vertexr^(Pred) is mapped to a second predicted vertex r^(RotPred). Theresulting first advanced prediction triangle Δur^(RotPred)v is mirroredat its co-planar local Y axis at (u+v)/2, i.e. in the middle between uand v, such that the mirrored triangle also has uv as one of its sides.The resulting mirrored triangle Δur^(AdvPred)v fully matches thespanning triangle T_(span) (or Δurv). In the next step it is determinedwhich of the three prediction triangles is the best: Δur^(Pred)v,Δur^(RotPred)v or Δur^(AdvPred)v. This is determined by comparing theirrespective residuals, and choosing the prediction triangle thatgenerates the smallest residual. Obviously it will be Δur^(AdvPred)v inthis case, since the residual is zero. Thus, for encoding the spanningtriangle T_(span) it is sufficient to identify the reference triangleT_(ref) and the edge uv (as usual in 3D mesh compression), the clusterto which the prediction belongs (thus identifying the dihedral angle)and the fact that mirror mapping is used. In other words, when thereference triangle T_(ref) and the edge uv are identified, the encodedspanning triangle T_(span) comprises only an indication of the cluster(one bit in this example, since there is only one cluster) and anindication of the mirror mapping step (one bit).

Though in this example the box is substantially rectangular, theinvention is still advantageous for other examples. However, in thatcase there will be more than one cluster, and therefore more bits arerequired for identifying a cluster. Additional bits are required forencoding the residuals for 3D meshes with less regular structure. In anycase, the invention is advantageous in every case where a limited rangeexists that includes many of the dihedral angles of the 3D mesh modeland that has substantially empty neighboring ranges. The advantageouseffect is the higher, the smaller the limited range is, the moredihedral angles use the range, and the larger the empty neighboringranges are. If more than one cluster is defined, the different clustersneed not have the same width. An example is shown in FIG. 13 a), asdescribed later.

FIG. 10 shows the general principle of improved triangle predictionusing mirrored prediction triangles. For a reference triangle T_(ref12)a parallelogram extension T_(aux12) is created, which is mapped by afirst rotation to a first prediction triangle T_(adv) _(—) _(pred1), asdefined by a first prediction vertex r_(adv) _(—) _(pred1). The firstprediction triangle T_(adv) _(—) _(pred1) is then mirrored to a secondprediction triangle T_(adv) _(—) _(pred2), as defined by a secondprediction vertex r_(adv) _(—) _(pred2).

Thus, it is equivalent to a mirror mapping of the first predictionvertex r_(adv) _(—) _(pred1) to a second prediction vertex r_(adv) _(—)_(pred2). All these triangles have a common side. The first rotation isaround the axis of the common side, by the dihedral angle θ₁₂. Forencoding, this is a representative dihedral angle determined accordingto the current 3D mesh model, as described above. For decoding, thisdihedral angle is predefined and may be received from any source, orextracted from received data, usually as a coding parameter of theencoded 3D mesh model. The second prediction triangle T_(adv) _(—)_(pred2) is obtained from the first prediction triangle T_(adv) _(—)_(pred1) by mirror mapping on its middle axis ax_(m12). This isequivalent to a rotation by 180° at this axis ax_(m12). As a result, thebase of the prediction triangle is mapped to itself (except that the endpoints are swapped).

Then the residuals res_(adv) _(—) _(pred1), res_(adv) _(—) _(pred2)between the spanning triangle T_(span) and both prediction trianglesT_(adv) _(—) _(pred1), T_(adv) _(—) _(pred2) are calculated, comparedwith each other and the residual that is easier/cheaper to encode (inthis case T_(adv) _(—) _(pred2)) is selected for predictive coding.

FIG. 11 shows examples of different dihedral angles, and the approximateposition of the resulting prediction triangles. In a first example, adihedral angle θ₁₂ at about 90° defines a first pair of predictiontriangles T_(adv) _(—) _(pred1), T_(adv) _(—) _(pred2), in a secondexample a dihedral angle θ₃₄ at about 200 degrees defines a second pairof prediction triangles T_(adv) _(—) _(pred3), T_(adv) _(—) _(pred4),and in a third example a dihedral angle θ₅₆ at about 300 degrees definesa third pair of prediction triangles T_(adv) _(—) _(pred5), T_(adv) _(—)_(pred6). Further, FIG. 11 shows the respective axes ax_(m12), ax_(m34),ax_(m56) that are used for the mirror mapping. Though the figures may benot exact in this respect, the axes are always orthogonal in the middleof the common side of the rectangles (also ax_(m34) although it may lookdifferent due to perspective), and co-planar with the predictiontriangles.

For those models with many sharp features, such as 3D engineeringmodels, the proposed advanced prediction scheme improves the geometrycompression efficiency significantly. The analysis step needs an extrascan of the geometry data which will slightly influence the encodingspeed. However, the amount of geometry data is reduced and the decoderspeed is hardly influenced by the advanced prediction.

By using those geometry-guided predictive schemes for compressing theconnectivity data of 3D meshes, the advanced prediction method proposedhere can further improve the efficiency of topology encoders, as thegeometry prediction is better.

Although the clustering generally depends on the individual 3D meshmodel, it may be useful to have predefined clustering ranges andrepresentative dihedral angles, e.g. for certain kinds of models. Inthis case, it is not necessary to transmit the representative angles, aslong as an unambiguous indication of the respective representativedihedral angle for the advanced prediction triangle is used. Also inthis case it is possible and advantageous to use mirror mapping.

The first prediction triangle and the second prediction triangle have acommon base side and are mirrored along an axis that is orthogonal totheir common base side, so that they have the same angles and sidelengths.

It depends on the details of the 3D mesh model how wide the range ofangles around the representative angle is. The range is generally small,for example five degrees or less, and the representative angle isusually the medium value of a cluster. Typically, a local maximum withinthe range can be defined. However, it is also possible that 3D meshmodels use mainly dihedral angles in a larger range. The invention canbe advantageous if the angles within this range are substantially evenlyspread, so that it is difficult to define a single local maximum withinthe range, and no dihedral angles are within comparable adjacent ranges.For example, a model may have many dihedral angles evenly spread in arange of 80-100 degrees, but no dihedral angles in ranges of 60-80 or100-120 degrees. On the other hand, if the dihedral angles are notsubstantially evenly spread within the range, it may be better to definetwo or more local maxima and assign each maximum its own range.

The 3D mesh model can also be partitioned into sub-models of appropriatesize, and each of the sub-models can be handled separately. In thiscase, the clustering and the representative dihedral angle are onlyvalid within a sub-model. This is advantageous e.g. if a part of a 3Dmesh model has significantly different surface structure than otherparts.

One particular advantage of the invention is that dihedral angles needonly be calculated between a next triangle and its respective referencetriangle. That is, each triangle has only one reference triangle, whichlimits the amount of computing.

FIG. 6 shows an encoder according to one aspect of the invention. Theencoder comprises a geometry encoder portion GE and an entropy encoderEE. The geometry encoder comprises a dihedral angle clustering moduleDAC, a prediction mode definition module PMD and an advancedparallelogram prediction module APP. The dihedral angle clusteringmodule DAC performs the analysis of the 3D mesh model, clustering ofdihedral angles and generation of representative dihedral angles (ifapplicable). The prediction mode definition module PMD defines for eachvertex the optimized encoding mode (either conventional, advanced basedon a representative angle or advanced based on a representative angleand mirroring) and the advanced parallelogram prediction module APPgenerates the residuals, wherein it applies the encoding mode that wasrespectively defined by the prediction mode definition module PMD. As aresult, prediction mode information PMI and prediction residualinformation PRI are provided to the entropy encoding unit EE, whichperforms entropy encoding and outputs entropy encoded data d_(out). Forexample, the entropy encoding unit EE may generate a data format with ageneral header, in which among others different representative dihedralangles are defined, and a separate data portion for each vertex. Thedata portion of a vertex comprises its respective prediction modeindication PMI and entropy encoded prediction residual data PRI.

FIG. 7 shows a decoder according to one aspect of the invention. Thedecoder comprises an entropy decoder portion ED and a geometry decoderportion GD. The entropy decoder receives entropy encoded input datad_(in), performs entropy decoding and provides to the geometry decoderportion GD prediction mode information PMI and prediction residualinformation PRI. The geometry decoder portion GD comprises a decodingversion of an advanced parallelogram prediction module APP′, andperforms prediction of the vertices according to their respectiveprediction mode information. The advanced parallelogram predictionmodule APP′ gets information about the representative dihedral anglesfrom a prediction mode reader unit RPM, which may e.g. extract thisinformation from the header of a received signal (not shown).

An example of a 3D mesh model is shown in FIG. 12. It was created with3DsMax and has 288 vertices and 572 triangles. While in FIG. 12 b) themeshes are visible, they are in FIG. 12 a) covered by texture. Thisexemplary model comprises a number of dihedral angles, which wereanalyzed and can be clustered as listed in Table 1. The most rightcolumn shows how many vertices use the corresponding mode.

TABLE 1 Prediction modes of “T” model Local Prediction Rotation MirrorMode Angle (Degree) Mapping? # 0 0 0 76 1 0 1 144 2 90 0 14 3 90 1 7 4355 0 31 5 355 1 0 6 350 0 13 7 350 1 0

As can be seen from Tab.1, only dihedral angles around 0°, 90°, 350° and355° appear. For each of them, a separate cluster is defined. Generally,the width of each cluster (i.e. the range of dihedral angles that fallinto it) can be individually different. Further, most vertices do notchoose prediction mode ‘0’, which is the traditional flat parallelogramprediction scheme. This is the result of choosing the optimizedresidual, and shows the advantage of the advanced parallelogrampredictor for compressing structures like the “T” model, even if thesurface is rather smooth.

The width of ranges may be different. FIG. 13 a) shows an exemplarydistribution of dihedral angles falling into a first range R₁ around afirst representative dihedral angle α₁ and into a different second rangeR₂ (R₁>R₂) around a second representative dihedral angle α₂. However, inmany artificially created 3D mesh models the ranges are very small,since only certain dihedral angles are used. FIG. 13 b) shows ahistogram of the seven encoding modes of Tab.1. As can be seen, not allpossible prediction modes are used. E.g. the dihedral angle of 350° isused only without mirror mapping (Local Mirror Mapping=0).

According to one aspect of the invention, bitstreams with encoded 3Dmesh models are enhanced in two levels:

First on geometry level, i.e. in the header of a group of vertex datathe prediction mode information includes:

-   -   one bit to indicate whether the proposed advanced parallelogram        predictor is used. E.g. “1” means the proposed prediction method        is employed, and “0” means that traditional solution is        employed.    -   some bits to indicate the number of prediction modes, e.g. one        byte. In the example of FIG. 13, the number of prediction modes        is eight, so bits “00001000” are inserted into the bitstream.    -   bits to show the detail of each prediction mode. E.g. each mode        uses 10 bits to represent its rotation angle, which is in the        range of 0-359°. Another bit is used to indicate whether mirror        mapping is used. Altogether 11 bits are used for each mode.

Second, on vertex level, i.e. in the header information of each vertex,the prediction mode information is added:

Few bits representing the prediction mode of the current vertex. E.g. 3bits are used for each vertex, sufficient for representing 8 modes.

For the above example, when using as entropy coder a range encoder⁴similar to the arithmetic or Huffman coder, it is possible to save about9% storage, since the prediction residual is greatly reduced. Bycarefully choosing the entropy encoder, especially the one forcompressing the prediction mode information, the gain can be furtherenlarged. This already takes into account that when using advancedparallelogram prediction scheme, the compressed geometry data includesnot only prediction residual but also prediction mode information.⁴“Range encoding: an algorithm for removing redundancy from digitizedmessage”, G. N. N. Martin, March 1979, Video & Data RecordingConference, Southampton, UK

The invention is advantageous for encoders and decoders, andparticularly for 3D mesh model encoders and decoders.

It will be understood that the present invention has been describedpurely by way of example, and modifications of detail can be madewithout departing from the scope of the invention. Each featuredisclosed in the description and (where appropriate) the claims anddrawings may be provided independently or in any appropriatecombination. Features may, where appropriate be implemented in hardware,software, or a combination of the two. Connections may, whereapplicable, be implemented as wireless connections or wired, notnecessarily direct or dedicated, connections. Reference numeralsappearing in the claims are by way of illustration only and shall haveno limiting effect on the scope of the claims. Drawings are notnecessarily in proportion of the actual dimensions.

1. A method for encoding a 3D mesh model composed of triangles, themethod comprising steps of determining pairs of triangles, each pairbeing a reference triangle and a triangle to be predicted, wherein bothtriangles have a common side along a first axis; for each of said pairsof triangles, determining a dihedral angle between the referencetriangle and the triangle to be predicted; analyzing for the 3D meshmodel the dihedral angles of the pairs of triangles and, based on saidanalyzing, defining at least a first range of dihedral angles, wherein aplurality of said dihedral angles are within the first range of dihedralangles; defining for said first range of dihedral angles a firstrepresentative dihedral angle; encoding the triangles of the 3D meshmodel, wherein residuals between reference triangles and correspondingpredicted triangles are determined and encoded, and wherein if thedihedral angle between a reference triangle and a correspondingpredicted triangle is within the first range of dihedral angles, saidencoding uses prediction based on an enhanced prediction triangle,wherein the dihedral angle between the reference triangle and theenhanced prediction triangle is said representative dihedral angle;calculating and encoding a residual between said triangle to bepredicted and said enhanced prediction triangle; and associating withthe encoded residual an indication indicating that it refers to saidrepresentative dihedral angle.
 2. Method according to claim 1, furthercomprising the step of associating with the encoded 3D mesh model avalue indicating said representative dihedral angle.
 3. Method accordingto claim 1, wherein a first enhanced prediction triangle of a first modeand a second enhanced prediction triangle of a second mode are mirroredalong a co-planar second axis that is orthogonal to said first axis,wherein the first and second enhanced prediction triangle have a commonside, and wherein a second indication is associated with the encodedresidual, the second indication indicating whether the residual refersto the prediction triangle of the first or the second mode.
 4. Methodaccording to claim 3, wherein in the first mode the enhanced predictiontriangle corresponds to a co-planar parallelogram extension of thereference triangle that is rotated by said representative dihedral angleon said first axis, and wherein the enhanced prediction triangles of thefirst and second mode are co-planar and both have said side along thefirst axis common with the reference triangle.
 5. Method according toclaim 3, wherein for the reference triangle two residuals according tothe two prediction modes are calculated based on the two co-planarenhanced prediction triangles, the method further comprising the stepsof comparing the two residuals; and selecting the residual that allowscheaper encoding of said reference triangle.
 6. Method according toclaim 1, wherein a plurality of ranges of dihedral angles and acorresponding plurality of representative dihedral angles are definedand used for prediction, and wherein said first indication indicates foreach residual also the representative dihedral angle to which theresidual refers.
 7. Method for decoding an encoded 3D mesh model beingcomposed of triangles, the method comprising steps of determining afirst representative dihedral angle; extracting from the encoded 3D meshmodel residual data relating to a reference triangle and to a triangleto be reconstructed, wherein the data have associated an indicationindicating a coding mode; decoding from the residual data a residualcomprising a residual triangle or residual vector; reconstructing thetriangle to be reconstructed based on a prediction from said referencetriangle, wherein the reference triangle and the reconstructed trianglehave a common side along a first 30 axis, and wherein in response tosaid indication a prediction mode is used that comprises combining theresidual with a predefined prediction triangle, wherein the dihedralangle between the reference triangle and the predefined predictiontriangle is said first representative dihedral angle.
 8. Methodaccording to claim 7, wherein said first representative dihedral angleis extracted from the encoded 3D mesh model.
 9. Method according toclaim 7, wherein in a first prediction mode the residual is added to afirst prediction triangle and in a second prediction mode the residualis added to a second prediction triangle, the first and secondprediction triangles having a common side with the reference trianglealong said first axis and being mirrored on a second axis that isorthogonal to said first axis.
 10. Signal comprising an encoded 3D meshmodel composed of triangles, the encoded 3D mesh model comprisingresidual data for a plurality of triangles, wherein the residual dataare suitable for reconstructing a next triangle based on a referencetriangle, wherein the reference triangle and the next triangle have acommon side, and wherein the residual data comprise an indicationindicating that the encoding of the next triangle is relative to aprediction triangle also having said common side, wherein the dihedralangle between the prediction triangle and the reference triangle is apredefined dihedral angle.
 11. Signal according to claim 10, wherein theresidual data further comprise an indication indicating whether saidencoding refers to a first or a second prediction triangle, wherein thesecond prediction triangle can be obtained from the first predictiontriangle by mirroring or rotating along a co-planar axis that isorthogonal on said common side.
 12. An apparatus for encoding a 3D meshmodel composed of triangles that are represented by connectivity data,geometry data and property data, the apparatus comprising firstdetermining means for determining pairs of triangles, each pair being areference triangle and a triangle to be predicted, wherein bothtriangles have a common side along a first axis; second determiningmeans for determining, for each of said pairs of triangles, a dihedralangle between the reference triangle and the triangle to be predicted;analyzing means for analyzing for the 3D mesh model the dihedral anglesof the pairs of triangles and, based on said analyzing, defining atleast a first range of dihedral angles, wherein a plurality of saiddihedral angles are within the first range of dihedral angles; definingmeans for defining for said first range of dihedral angles a firstrepresentative dihedral angle; encoding means for encoding the trianglesof the 3D mesh model, wherein residuals between reference triangles andcorresponding predicted triangles are determined and encoded, andwherein if the dihedral angle between a reference triangle and acorresponding predicted triangle is within the first range of dihedralangles, said encoding uses prediction based on an enhanced predictiontriangle, wherein the dihedral angle between the reference triangle andthe enhanced prediction triangle is said representative dihedral angle;for calculating and encoding a residual between said triangle to bepredicted and said enhanced prediction triangle; and for associatingwith the encoded residual an indication indicating that it refers tosaid representative dihedral angle.
 13. Apparatus according to claim 12,wherein a first enhanced prediction triangle of a first mode and asecond enhanced prediction triangle of a second mode are mirrored alonga co-planar second axis that is orthogonal to said first axis, whereinthe first and second enhanced prediction triangle have a common side,and wherein a second indication is associated with the encoded residual,the second indication indicating whether the residual refers to theprediction triangle of the first or the second mode.
 14. An apparatusfor decoding an encoded 3D mesh model being composed of triangles, theapparatus comprising first determining means for determining a firstrepresentative dihedral angle; first extracting means for extractingfrom the encoded 3D mesh model residual data relating to a referencetriangle and to a triangle to be reconstructed, wherein the data haveassociated an indication indicating a coding mode; decoding means fordecoding from the residual data a residual comprising a residualtriangle or residual vector; reconstructing means for reconstructing thetriangle to be reconstructed based on a prediction from said referencetriangle, wherein the reference triangle and the reconstructed trianglehave a common side along a first axis, and wherein in response to saidindication a prediction mode is used that comprises combining theresidual with a predefined prediction triangle, wherein the dihedralangle between the reference triangle and the predefined predictiontriangle is said first representative dihedral angle.
 15. Apparatusaccording to claim 14, further comprising second extracting means forextracting a second indication from the encoded residual, wherein thereconstructing means for reconstructing the triangle to be reconstructedhas at least a first and a second prediction mode and the secondindication indicates whether a residual refers to a prediction triangleof the first or the second mode, wherein in the first prediction modethe residual is added to a first prediction triangle and in the secondprediction mode the residual is added to a second prediction triangle,the first and second prediction triangles having a common side with thereference triangle along said first axis and being mirrored on a secondaxis that is orthogonal to said first axis.